Counterparty default risk might hamper trade and trigger a financial crisis. The introduction of a central clearing counterparty (CCP) benefits trading but pushes systemic risk into CCP default. Standard risk management strategies at CCPs currently overlook a risk associated with crowded trades. This paper identifies it, measures it, and proposes a margin methodology that accounts for it. The application to actual CCP data illustrates that this hidden risk can become large, in particular at times of high CCP risk.